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Sibirsk. Mat. Zh., 2007, Volume 48, Number 1, Pages 192–204 (Mi smj16)  

This article is cited in 5 scientific papers (total in 5 papers)

On lattices embeddable into subsemigroup lattices. III: Nilpotent semigroups

M. V. Semenova

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: We prove that the class of the lattices embeddable into subsemigroup lattices of $n$-nilpotent semigroups is a finitely based variety for all $n<\omega$. Repnitskii showed that each lattice embeds into the subsemigroup lattice of a commutative nilsemigroup of index 2. In this proof he used a result of Bredikhin and Schein which states that each lattice embeds into the suborder lattices of an appropriate order. We give a direct proof of the Repnitskii result not appealing to the Bredikhin–Schein theorem, so answering a question in a book by Shevrin and Ovsyannikov.

Keywords: lattice, semigroup, sublattice, variety.

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English version:
Siberian Mathematical Journal, 2007, 48:1, 156–164

Bibliographic databases:

UDC: 512.56
Received: 18.10.2005

Citation: M. V. Semenova, “On lattices embeddable into subsemigroup lattices. III: Nilpotent semigroups”, Sibirsk. Mat. Zh., 48:1 (2007), 192–204; Siberian Math. J., 48:1 (2007), 156–164

Citation in format AMSBIB
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\paper On lattices embeddable into subsemigroup lattices. III: Nilpotent semigroups
\jour Sibirsk. Mat. Zh.
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\pages 192--204
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\jour Siberian Math. J.
\yr 2007
\vol 48
\issue 1
\pages 156--164
\crossref{https://doi.org/10.1007/s11202-007-0016-2}
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    This publication is cited in the following articles:
    1. M. V. Semenova, “Lattices Embeddable in Subsemigroup Lattices. I. Semilattices”, Algebra and Logic, 45:2 (2006), 124–133  mathnet  crossref  mathscinet  zmath
    2. M. V. Semenova, “Lattices Embeddable in Subsemigroup Lattices. II. Cancellative Semigroups”, Algebra and Logic, 45:4 (2006), 248–253  mathnet  crossref  mathscinet  zmath
    3. M. V. Semenova, “On lattices embeddable into subsemigroup lattices. V. Trees”, Siberian Math. J., 48:4 (2007), 718–732  mathnet  crossref  mathscinet  zmath  isi
    4. Semenova M.V., “On lattices embeddable into subsemigroup lattices. IV. Free semigroups”, Semigroup Forum, 74:2 (2007), 191–205  crossref  mathscinet  zmath  isi  elib  scopus
    5. M. V. Semenova, “Embedding Lattices into Derived Lattices”, Proc. Steklov Inst. Math., 278, suppl. 1 (2012), S116–S130  mathnet  crossref  crossref  isi  elib
  • Сибирский математический журнал Siberian Mathematical Journal
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